





"""simple docstring"""





from __future__ import annotations

import math


def      UpperCAmelCase__				(    SCREAMING_SNAKE_CASE	:		int				,		SCREAMING_SNAKE_CASE	:		int				,		SCREAMING_SNAKE_CASE	:		bool				,		SCREAMING_SNAKE_CASE	:		list[int]				,		SCREAMING_SNAKE_CASE	:		float     ):







      '''simple docstring'''




      if depth < 0:
            raise ValueError("""Depth cannot be less than 0"""     )

      if not scores:
            raise ValueError("""Scores cannot be empty"""     )

      if depth == height:
            return scores[node_index]

      return (
          max(
              minimax(depth + 1				,		node_index * 2				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE     )				,		minimax(depth + 1				,		node_index * 2 + 1				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE     )				,		)
          if is_max
          else min(
              minimax(depth + 1				,		node_index * 2				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE     )				,		minimax(depth + 1				,		node_index * 2 + 1				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE     )				,		)
      )


def      UpperCAmelCase__				(    ):







      '''simple docstring'''




      lowerCAmelCase    		=			[90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
      lowerCAmelCase    		=			math.log(len(SCREAMING_SNAKE_CASE     )				,		2     )
      print(F'Optimal value : {minimax(0				,		0				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE				,		SCREAMING_SNAKE_CASE     )}'     )


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       main()













"""simple docstring"""





from math import log

from scipy.constants import Boltzmann, physical_constants

SCREAMING_SNAKE_CASE__   =  300  # TEMPERATURE (unit = K)


def      UpperCAmelCase__				(    SCREAMING_SNAKE_CASE	:		float				,		SCREAMING_SNAKE_CASE	:		float				,		SCREAMING_SNAKE_CASE	:		float				,		):







      '''simple docstring'''




      if donor_conc <= 0:
            raise ValueError("""Donor concentration should be positive"""     )
      elif acceptor_conc <= 0:
            raise ValueError("""Acceptor concentration should be positive"""     )
      elif intrinsic_conc <= 0:
            raise ValueError("""Intrinsic concentration should be positive"""     )
      elif donor_conc <= intrinsic_conc:
            raise ValueError(
                """Donor concentration should be greater than intrinsic concentration"""     )
      elif acceptor_conc <= intrinsic_conc:
            raise ValueError(
                """Acceptor concentration should be greater than intrinsic concentration"""     )
      else:
            return (
                Boltzmann
                * T
                * log((donor_conc * acceptor_conc) / intrinsic_conc**2     )
                / physical_constants["electron volt"][0]
            )


if __name__ == "__main__":
       import doctest

       doctest.testmod()






